In this case "it's not on me" means something like ' it's not my decision' . 'It's not my decision to let you do anything' =)

kinda weird sentence... although "i'ts on me" may mean "It's my responsibility" or "It's my call", I'm not pretty sure of these phrase were correctly used in your paragraph. I think "It's not on me to let you do anything." may imply that the speaker is not the one to asked for the doer's action. It may answer the question : "why are you asking me?" :)

Yes, it's a bit unusual to the Aussie ear. :) I'd understand it as, "the responsibility (=it) is not on me."

Agreed with Jennifer :)

I guess something like 'it's not up to me', it's (for does) not depend on me'? Or maybe just a typo - 'it's not me to...' incorrect either though. Obviously it's quite colloquial, not formal if you're sure it was said like that - the listener was able to understand this sentence being into the context though.